I consider deep learning to be in the family of statistical methods. The problem with previous statistical methods is that they were shallow and couldn't learn very complicated functions or structure. No one ever claimed that linear regression would lead to AGI.

I'm not aware of great success in Go? 54% accuracy is very hard to interpret in a vaccuum in terms of how impressed to be.

That narrows the search space to maybe 2 moves or so per board. Which makes heuristic searching algorithms much more practical. You can not only generate good moves and predict what a human will do, but you can combine that with brute force and search much deeper than a human as well.

And neural nets definitely need heuristics

I mean that NNs learn heuristics. They do require heuristics in the learning algorithm, but not ones that are specific to the domain. Whereas search algorithms depend on lots of domain dependent, manually created heuristics.